Question

You run a regression of monthly returns of Mapco, an oil- and gas-producing firm, on the S&P 500 Index and come up with the following output for the period 1991 to 1995. Intercept of the regression = 0.380%; X-coefficient of the regression =0.55; Standard error of X-coefficient =0.2; R2=55.0% There are 18.00 million shares outstanding, and the current market price is $6.00/share. The firm has $20.00million in debt outstanding. The firm has a tax rate of 40.00% percent.

b. Assume now that Mapco has three divisions. It plans to divest itself of one of the divisions for $22.00 million in cash and acquire another for $67.00 million (it will borrow $45.00 million to complete this acquisition). The division it is divesting is in a business line where the average unlevered beta is 0.35, and the division it is acquiring is in a business line where the average unlevered beta is 0.88. What will the beta of Mapco be after this acquisition?

2.Unlevered beta of Mapco before restructuring?

3.Current firm size?

4.Unlevered beta of the remaining divisions?

5.Firm size after restructuring (i.e. after divesting a division and acquiring the new division)?

6.Total debt after restructuring (i.e., after divesting one division and purchasing a new division)?

7.Unlevered beta after restructuring?

8.Levered beta after restructuring

Answer #1

Levered Beta from the regression equation = 0.55

Equity value = 6*18million = 108 million

Debt = 20 million

Firm Value = 108+20 = 128 million

Debt/Equity = 20/108 = 0.185

Unlevered Beta = Levered Beta/(1+(1-Tax)*(D/E))

Unlevered Beta = 0.55/(1+(1-40%)*(20/108)) = 0.495

Beta of firm = (Value of division 1*Beta of Division 1 + Value of division 2*Beta of Division 2+Value of division 3*Beta of Division 3)/ Total firm value

Unlevered Beta after divestment be X

0.35*(22/128) + X*(106/128) = 0.495

X = 0.5251

New Firm Size = Existing firm size + Additional Borrowing for investment

= 128+45 = 173

Total Debt = 20+45 = 65 million

Unlevered beta after restructuring = 0.5218*(106/173) + 0.88*(67/173) = 0.6605

Levered Beta = 0.6605*(1+(1-40%)*(65/108)) = 0.899

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